An analytical performance modeling approach for supply chain networks (SCNs) is developed based on the parametric decomposition method. The upstream flow of demand information and the downstream flow of material are analyzed to derive the arrival process parameters at various inventory points in a SCN. A sequential solution procedure that proceeds from the supplier stage to the retailer stage is then developed. The backorder distribution plays a key role in linking probability calculations between adjacent stages in the SCN model. This sequential procedure can be used to derive the inventory and backorder distributions at various inventory points in the SCN, when specific models are chosen for the SCN components, namely, suppliers, transportation operations, and manufacturers. An example SCN with three suppliers, two manufacturers, and three retailers is used to illustrate the modeling approach. The accuracy of the analytical results is evaluated by comparison with simulation estimates. The approach developed yields computationally efficient and numerically accurate analytical models that are especially useful in addressing SCN design issues.

We discuss the importance of P-invariant analysis of Petri nets and its relationship to the controllability and boundedness of the same. We discuss why a Petri net cannot be fully controllable and bounded simultaneously. It is often mentioned in literature that the rank of the incidence matrix of a Petri net is the difference between the number of places and the number of minimal place invariant sets in the Petri net. We introduce a counterexample in which the above relationship is not true, and then point out the reason for the discrepancy. The discrepancy arises because of the nonnegativity restriction imposed by the definition of the place invariant sets.

In synchronous production lines, the transfer of all parts in the line takes place simultaneously. If one workstation breaks down, the whole line will be shut down for repair. The authors consider modeling the performance of such lines with random line stoppages, scrapping of parts, and a limited number of operators available for clearing workstations. An analytical model is proposed for this purpose. In the single operator case, the model is free of any distributional assumptions. For the multiple operator case, an exponential assumption is required for an exact analysis, but simple performance bounds are derived for the general case. Some numerical examples are presented.>

Petri nets have evolved into a powerful tool for analyzing asynchronous concurrent systems. In this paper we review the applications of Petri nets to FMSs. We present applications of Petri net models in the design of simulators for flexible manufacturing systems (FMSs) and in the verification (by investigating the presence/absence of deadlock) of the logic used to design the hardware/software for controllers used in FMSs.